Consolidated Metals manufactures only ashtrays and umbrella

I considered 40 ashtrays and 60 umbrellas in 1983. Played around with the answer choices and concluded that A is the answer.

Dear Friends,
A closer look at the answer choices reveal that the author of the question wants to gauge the clarity of understanding of the relation between the argument and the correct answer.

My approach to answer the question:

I refuted the choices C and D on the pretext of poor association with the argument.
Proceeding further to choices B and E I approached them as below:

We cannot comment on the numbers of Ashtrays and Umbrella stands manufactured by the company since the comparison is between the Percentage of 1983 and numeric increase in 1993.
This can be derived by considering a sample data:
1983: 100 units manufactured overall: 40 units AT[Ashtrays] and 60 units US[Umbrella stands].
1984:
Now referring to the argument we can have
1.US production increased by 10 percent.In this case we shall have 66 units of US produced and AT increased by even more which may result in 70 units . Here % of US >% of AT
Or we can have
2. US production increased by 150 percent ,which accounts to 150 units and the AT production increased by more than 150-60=90 units ,lets say AT's production was 100 units in 1993.Here % of US < % of AT

Referring to 1 and 2 above we can refute choice B and E also.

Choice A in all cases will hold true as the production percentage dedicated to ashtrays will be greater than 40 % as the increase in AT's production is always greater than corresponding US's production quantity increase.

Hope that helps
Cheers,
Rohan

x->Total Production in 1983
y->Extra Production in 1993
GT->Greater than
LT->Less than

Ash(1983)=0.4x Vs Umbrella(1983)=0.6x
Ash(1993)=0.4x+GT(0.5y) Vs Umbrella(1993)=0.6x+LT(0.5y)
Ashtray(1993)=GT(0.4(x+y))

Ans: "A"

A. In 1993, the percentage of Consolidated Metal's production devoted to ashtrays was greater than that in 1983. - sounds right to me, bcoz the Q states that the production of no. ashtray had increased over the ten year period.

E. In 1993, Consolidated Metals produced more ashtrays than umbrella stands. - can be dismiss this by saying that - there is no mention about the no. of umbrellas to ashtrays produced in 1993, since we only talk about ashtrays increase over ten year period

if some one could explain the line of reasoning more elaborately, it would be great

as of B,C and D, they seem out of scope.

Ans. A (not sure if my reasoning is right)

"A" says: In 1993, the total count of ashtrays produced accounted for more than 40% of the total production of Ashtrays & Umbrella.

In 1983: We know Ashtrays accounted for exactly 40% of the total production.
In 1993: Using the given information, we can conclude that Ashtrays accounted for at least more than 40% of the total production.

I got confused in this question:
83: 40 ashtray and 60 umbrella
93: Umbrella > 60(more than 83), then ashtray < 40. Something is wrong, I am missing something here.

Hi,
Instead of focusing on answer choice A , try to eliminate other choices ( which is easy) and you will be left with only answer A. Coming to your doubt .

Lets say
In 83 : Astray 40 ; Umbrella 60 .
In 93 : Astray 100 ( 60 increased) and Umbrella : 100 ( 40 Increased).

As number of astray has increased more than number of umbrella.

Percentage of astray in 83 : 40
Percentage of astray in 93 : 50

Therefore answer is A.

Consolidated Metals manufactures only ashtrays and umbrella stands. In 1983, ashtrays accounted for 40 percent of their production. In 1993 they produced more umbrella stands than in 1983, but the increase in the number of ashtrays they produced was even greater over the same ten year period.

If all the facts above are true, which of the following must also be true? <-- sounds like an INFERENCE

A. In 1993, the percentage of Consolidated Metal's production devoted to ashtrays was greater than that in 1983.
- If percentage of ashtrays in 83 = 40%, and CM increases the # of ashtrays substantially, it has to be over 40%

B. In 1993, Consolidated Metals produced fewer ashtrays than umbrella stands.
- "Fewer" = tricky word here. We're not given actual numbers in the passage, so it's hard to say without more info

C. In 1993, ashtrays were more cost-efficient to produce than they were in 1983
- Out of scope. Where does the passage mention which item was more cost-effective? Nowhere.

D. The production of umbrella stands required more labor in 1993 than did ashtrays in 1983.
- Out of scope. What does the passage mention about labor? Nothing.

E. In 1993, Consolidated Metals produced more ashtrays than umbrella stands.
- Does not HAVE to be true. Why? Because you know that the # of umbrella stands in 83 could be significantly more than the # of ashtrays. Think about it: this is 40v60. Let's expand that out -- 4,000,000 v 6,000,000. If 4m increased to 5m but 6m increased to 6.5m, it is correct to say that 4m increased more, but it is incorrect to say that they produced more of it.

i think what makes this question tricky (and time-consuming) is switching between % and absolute #s.
> However, if we use POE to get rid of out of scope A/C and if we scope out this change, we're left with a 50/50 shot between A & E.
>> From here, it may help to pick #s and create a visual situation in your head

Kudos please if you find this helpful

The correct answer is option (A).


Understanding the passage:

There are two ways to solve this. One is algebraic (using variables) but that may be too complex in a timed environment. The easier way is to assume values.

My approach
Now, when we assume values, we need to be careful to cover all possible scenarios.

When we assume values, we need to cover

1. A lower extreme set
2. A typical mid range set
3. A higher extreme set

A true inference should hold true across all 3 sets of assumed values.

For this problem, let us assume -

Total Production in 1983 = 100; then
Ashtray Production = 40
Umbrella Stand Production = 60

Given increase in ashtray production (A) > increase in umbrella stand production (U)

i.e. A > U

3 extremes:

1) A just > U say A =2, U = 1 (Bare minimum possible)

Now Ashtray Production (1993) = 40+ 2 = 42
US Production = 60+1 = 61

What can we infer:
1. Ashtray production < Umbrella Stand Production
2. % Contribution of Ashtray Production = (42) / (42+61) = 40.7% . Greater than the same metric in 1983 (40%)

2) A > U say A = 30, U = 20

Now Ashtray Production (1993) = 40+ 30 = 70
US Production = 60+20 = 80

What can we infer:
1. Ashtray production < Umbrella Stand Production
2. % Contribution of Ashtray Production = (70) / (70+80) = 47% . Greater than the same metric in 1983 (40%)

3) A >>> U say A = 90, U = 10

Now Ashtray Production (1993) = 40+ 90 = 130
US Production = 60+10 = 70

What can we infer:
1. Ashtray production > Umbrella Stand Production (notice this has changed)
2. % Contribution of Ashtray Production = (130) / (130+70) = 65% . Greater than the same metric in 1983 (40%)

Now, let us look at the answer choices:

A. In 1993, the percentage of Consolidated Metal's production devoted to ashtrays was greater than that in 1983.

Valid inference (our inference 2). We have seen above that whatever the assumed values, this holds true.

B. In 1993, Consolidated Metals produced fewer ashtrays than umbrella stands.

Not valid in our 3rd set of assumed values (higher extreme). Hence, we cannot infer this.

C. In 1993, ashtrays were more cost-efficient to produce than they were in 1983

Irrelevant. The passage does not talk about this entity (cost efficiency). Hence, we can't make any inference about this.

D. The production of umbrella stands required more labor in 1993 than did ashtrays in 1983.

Irrelevant. The passage does not talk about this entity (labour). Hence, we can't make any inference about this.

E. In 1993, Consolidated Metals produced more ashtrays than umbrella stands.

Not valid in our 1st and 2nd set of assumed values. Hence, we cannot infer this.


Hope this helps.
Cheers!

The correct Answer is A.

To explain the reasoning, we know from the passage that Consolidated Metals produced more umbrella stands in 1993 than in 1983, but they also produced even more ashtrays than they did in 1983. This means that the percentage of production devoted to ashtrays in 1993 may or may not be greater than it was in 1983.

However, we do know that the total production of ashtrays increased more than the production of umbrella stands over the same period of time. Therefore, it must be true that the percentage of Consolidated Metal's production devoted to ashtrays was greater in 1993 than in 1983. So, the correct answer is A.

Option B is incorrect because the passage does not give any information about the number of ashtrays or umbrella stands produced in 1993, only that there was an increase in both from 1983. Option C is incorrect because the passage does not provide any information about the cost efficiency of producing ashtrays. Option D is incorrect because the passage does not provide any information about the labor required to produce ashtrays or umbrella stands. Finally, option E may or may not be true, as we do not know the exact numbers for the production of ashtrays and umbrella stands in 1993.